Prior to the background of the invention being set forth, it may be helpful to set forth definitions of certain terms that will be used hereinafter.
The term ‘media’ or ‘medium’ as used herein is defined as material(s), subject(s) or object(s) such as an homogeneous or close to homogenous material in which scaterrers may be present in and may be for example air, concrete, plaster, fluids human tissues etc.
The term ‘ϵ_R’ (relative permittivity), refraction index (n), and propagation velocity (denoted v) as used herein and through the specification and claims should be used interchangeably, since in non-ferromagnetic materials they are related by the Eq v=c/n, n=√(ϵ_R), where c is the speed of light. However this is merely a convenience which does not limit the scope of the invention.
The term ‘velocity factor’ (hereinafter wave propagation speed or velocity of propagation (VoP or v_P) of a transmission medium as used herein and through the specification and claims is the ratio of the speed at which a wavefront (of an acoustic signal, for example, or an electromagnetic signal, a radio signal, a light pulse in a fibre channel or a change of the electrical voltage on a copper wire) passes through the medium, to the speed of light in a vacuum. For optical signals, the velocity factor is the reciprocal of the refractive index.
The term ‘reflector’ or scattering object herein and through the specification and claims should be defined as any object reflecting all or part of the incident (e.g. electromagnetic) wave. The detection or imaging of objects through media is a challenging task which requires advanced and sophisticated electronic imaging systems. The media may be defined as
Known methods and systems of imaging such as confocal imaging of reflective targets in homogenous or layered media using a set of active measurements such as antenna array and/or SAR (Synthetic Aperture Radar) scanning requires prior knowledge of the media parameters. Primarily the major parameter which must be known is a propagation velocity (associated with the reflective index or dielectric permittivity) in order to back-propagate and focus all reflections from a given target at the same point.
Other media parameters, such as loss (attenuation, e.g. due to conductivity) and dispersion (i.e. varying parameters over frequency) are also important for imaging and have to be estimated. For example, knowledge of the loss parameters is important in order to scale received signals correctly, and distinguish targets which have a weak reflection from those who suffered significant path loss.
Knowledge of the media parameters may be important on its own and not only as a parameter for imaging; for example, characterization of the material(s) of which a wall is made, or properties of fluid in a pipe.
Furthermore, the media can be non-homogenous but in a way that enables the identification of homogenous regions. The most pertinent example is layered media where the layers extend in the directions parallel to the array. For example a layer of stucco followed by concrete (where dielectric parameters and layer depth are unknown and need to be estimated).
In the field of SAR there are a number of known solutions for estimation of unknown parameters, via autofocusing of the resulting image, for example as illustrated in an article titled “SYNTHETIC APERTURE IMAGING AND AUTOFOCUS WITH COHERENT MIMO SONAR SYSTEMS” by Yan Pailhas and Yvan Petillot, OSL, Heriot Watt University, Edinburgh, UK and in article titled “Synthetic-aperture radar autofocus by maximizing sharpness” by J. R. Fienup (Feb. 15, 2000/Vol. 25, No. 4/OPTICS LETTERS) Yvan Petillot, [Yegulalp 1999], [Fienup 2000])).
In the case of SAR, in the context of large distances (kilometers) where the interface is air (non dielectric) the main effort of autofocusing is to correct errors in the antenna locations. As opposed to solutions based on the image itself, PGA (phase gradient autofocus) utilizes the measurements in a more direct fashion (for example as illustrated in the article: “EXPANSIONS AND DISCUSSIONS OF THE PHASE GRADIENT ALGORITHM” by James Stewart Bates [D. Wahl]), to solve the same problem. Some authors suggest using autofocus algorithms to estimate and correct the target velocity (not the propagation velocity) as for example illustrated in an article titled “SYNTHETIC APERTURE IMAGING AND AUTOFOCUS WITH COHERENT MIMO SONAR SYSTEMS” by Yan Pailhas and Yvan Petillot and also in article titled: “Retrospective Motion Correction” by David Atkinson.
Estimation of media velocity may be found in respect to sonar applications. Mainly, estimation of media velocity found in literature is treated as an inverse problem, i.e. the aim is to find a full characterization of a possibly inhomogenous medium which would have produced reflected signals close to the ones measured. An example of such solution may be found in an article titled: “Full Waveform Inversion Using One-way Migration and Well Calibration” by Gary F. Margrave, Robert J. Ferguson, and Chad M. Hogan and in article titled “Estimation of the Frequency-Dependent Average Dielectric Properties of Breast Tissue Using a Time-Domain Inverse Scattering Technique” by David W. Winters).
In the field of seismic measuring, seismic signals are typically compared using travel time difference or L2 difference. According to prior art solutions a Wasserstein metric provided is as an alternative measure of fidelity or misfit in seismology. The numerical computation is based on fast numerical methods for the Monge-Amp'ere equation and optimal transport. An example of such solution may be found in an article titled: ‘APPLICATION OF THE WASSERSTEIN METRIC TO SEISMIC SIGNALS’ by BJORN ENGQUIST and BRITTANY D. FROESE.